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GUJCET · Maths · Inverse Trigonometric Functions
\(\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]=\) ___________.
- A \(-\frac{\pi}{4}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{3\pi}{4}\)
- D \(-\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\( \tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right] = \tan ^{-1}\left[2 \cos \left(2 \cdot \frac{\pi}{6}\right)\right] \) \( = \tan ^{-1}\left[2 \cos \left(\frac{\pi}{3}\right)\right] \)
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